Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #31826873 | C2 | semidirect |
| 3. #31826869 | C2 | semidirect |
| 4. #31826866 | C2 | semidirect |
| 29. #17985376 | Q8 | semidirect |
| 44. C2×C8×C283 | Q8 | semidirect |
| 80. C283 | #3164 | semidirect |
| 114. C2×C8 | Dic566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827096 | 2 |
| #31826873 | 2 |
| #31826869 | 2 |
| #31826866 | 2 |
| #31826505 | 2 |
| #31826503 | 2 |
| #31826420 | 2 |
| C2×#107×C283 | 2 |
| #3164 | 283 |